Problem: Solve for $x$ and $y$ using elimination. ${-3x-3y = -48}$ ${3x-4y = -22}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3x$ and $3x$ cancel out. $-7y = -70$ $\dfrac{-7y}{{-7}} = \dfrac{-70}{{-7}}$ ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {-3x-3y = -48}\thinspace$ to find $x$ ${-3x - 3}{(10)}{= -48}$ $-3x-30 = -48$ $-3x-30{+30} = -48{+30}$ $-3x = -18$ $\dfrac{-3x}{{-3}} = \dfrac{-18}{{-3}}$ ${x = 6}$ You can also plug ${y = 10}$ into $\thinspace {3x-4y = -22}\thinspace$ and get the same answer for $x$ : ${3x - 4}{(10)}{= -22}$ ${x = 6}$